RRPP (version 2.0.3)

coef.lm.rrpp: coef for lm.rrpp model fits

Description

Computes ordinary or generalized least squares coefficients over the permutations of an lm.rrpp model fit with predefined random permutations. For each coefficient vector, the Euclidean distance is calculated as an estimate of the amount of change in Y, the n x p matrix of dependent variables; larger distances mean more change in location in the data space associated with a one unit change in the model design, for the parameter described. Random coefficients are based on either RRPP or FRPP, as defined by the lm.rrpp model fit.

This function can be used to test the specific coefficients of an lm.rrpp fit. The test statistics are the distances (d), which are also standardized (Z-scores). The Z-scores might be easier to compare, as the expected values for random distances can vary among coefficient vectors.

If RRPP is used, all distributions of coefficient vector distances are based on appropriate null models, as defined by SS type. Please be aware that this can result in two seemingly strange but reasonable phenomena. First, if type II or type III SS is used, the intercept will not appear in test results (because the function seeks model parameter differences to know for which coefficients to calculate Euclidean distances). Even if it appears for type I SS, this is merely an artifact of sequential model building and there really is no meaningful test of intercept = 0. Second, Euclidean distances might not always be logical, especially when viewing univariate coefficients, in which case the expected d is |b|. Coefficients without a test are based on the full model; tests are based on the estimates of coefficients (b), given a null model. For example, for a model, y ~ b1 + b2 + b3, with type I SS, b2 will be estimated and tested, using a null model, y ~ b1 and a full model, y ~ b1 + b2. The estimate for b2 might not be the same in the test as when estimated from the model, y ~ b1 + b2 + b3. Therefore, the d statistic might not reflect what one would expect from the full model (like when using type III SS).

Usage

# S3 method for lm.rrpp
coef(object, SE = FALSE, test = FALSE, confidence = 0.95, ...)

Arguments

object

Object from lm.rrpp

SE

Whether to include standard errors of coefficients. Standard errors are muted if test = TRUE.

test

Logical argument that if TRUE, performs hypothesis tests (Null hypothesis is vector distance = 0) for the observed coefficients. If FALSE, only the observed coefficients are returned.

confidence

The desired confidence limit to print with a table of summary statistics, if test = TRUE. Because distances are directionless, confidence limits are one-tailed.

...

Other arguments (currently none)

Author

Michael Collyer

Examples

if (FALSE) {
# See examples for lm.rrpp to see how anova.lm.rrpp works in conjunction
# with other functions

data(Pupfish)
names(Pupfish)
Pupfish$logSize <- log(Pupfish$CS)

fit <- lm.rrpp(coords ~ logSize + Sex*Pop, 
SS.type = "I", data = Pupfish, verbose = TRUE) 

coef(fit) # Just coefficients
coef(fit, SE = TRUE) # Coefficients with SE
coef(fit, test = TRUE, 
confidence = 0.99) # Test of coefficients
}